Question: Factor the following expression: $7$ $x^2$ $-13$ $x$ $-2$
Answer: This expression is in the form ${A}x^2 + {B}x + {C}$ . You can factor it by grouping. First, find two values, $a$ and $b$ , so: $ \begin{eqnarray} {ab} &=& {A}{C} \\ {a} + {b} &=& {B} \end{eqnarray} $ In this case: $ \begin{eqnarray} {ab} &=& {(7)}{(-2)} &=& -14 \\ {a} + {b} &=& & & {-13} \end{eqnarray} $ In order to find ${a}$ and ${b}$ , list out the factors of $-14$ and add them together. Remember, since $-14$ is negative, one of the factors must be negative. The factors that add up to ${-13}$ will be your ${a}$ and ${b}$ When ${a}$ is ${1}$ and ${b}$ is ${-14}$ $ \begin{eqnarray} {ab} &=& ({1})({-14}) &=& -14 \\ {a} + {b} &=& {1} + {-14} &=& -13 \end{eqnarray} $ Next, rewrite the expression as ${A}x^2 + {a}x + {b}x + {C}$ $ {7}x^2 +{1}x {-14}x {-2} $ Group the terms so that there is a common factor in each group: $ ({7}x^2 +{1}x) + ({-14}x {-2}) $ Factor out the common factors: $ x(7x + 1) - 2(7x + 1) $ Notice how $(7x + 1)$ has become a common factor. Factor this out to find the answer. $(7x + 1)(x - 2)$